The Solar Hijri calendar (Persian: گاه‌شماری هجری خورشیدی‎, Pashto: لمريز لېږدیز کلیز‎), also called the Solar Hejri calendar[1] or Shamsi Hijri calendar, and abbreviated as SH, is the official calendar of Iran and Afghanistan. It begins on the vernal equinox as determined by astronomical calculation for the Iran Standard Timemeridian (52.5°E or GMT+3.5h). This determination of starting moment is more accurate than the Gregorian calendar for predicting the date of the vernal equinox, because it uses astronomical observations rather than mathematical rules.[2]

On 21 February 1911, the second Persian parliament adopted as the official calendar of Iran the Jalālī sidereal calendar with months bearing the names of the twelve constellations of the zodiac and the years named for the animals of the duodecennial cycle; it remained in use until 1925.[1] The present Iranian calendar was legally adopted on 31 March 1925, under the early Pahlavi dynasty. The law said that the first day of the year should be the first day of spring in "the true solar year", "as it has been" ever so. It also fixed the number of days in each month, which previously varied by year with the sidereal zodiac. It revived the ancient Persian names, which are still used. It specified the origin of the calendar (Hegira of Muhammad from Mecca to Medina in 622 CE). It also deprecated the 12-year cycles of the Chinese-Uighur calendar which were not officially sanctioned but were commonly used.

The first six months (Farvardin–Shahrivar) have 31 days, the next five (Mehr–Bahman) have 30 days, and the last month (Esfand) has 29 days or 30 days in leap years. This is a simplification of the Jalali calendar, in which the commencement of the month is tied to the sun's passage from one zodiacal sign to the next. The sun is travelling fastest through the signs in early January (Dey) and slowest in early July (Tir). The current time between the vernal equinox and the autumnal equinox is about 186 days and 10 hours, the opposite duration about 178 days, 20 hours).

The Solar Hijri calendar (Persian: گاهشماری هجری خورشیدی‎) produces a five-year leap year interval after about every seven four-year leap year intervals. It usually follows a 33-year cycle with occasional interruptions by single 29-year or 37-year subcycles. The reason for this behaviour is (as explained above) that it tracks the observed vernal equinox. By contrast, some less accurate predictive algorithms are suggestion based on confusion between average tropical year (365.2422 days, approximated with near 128-year cycles or 2820-year great cycles) and the mean interval between spring equinoxes (365.2424 days, approximated with a near 33-year cycle).

In 1976, Shah Mohammad Reza Pahlavi changed the origin of the calendar, using the beginning the reign of Cyrus the Great as the first day, rather than the Hejra of Muhammad. Overnight, the year changed from 1355 to 2535. The change lasted till the Islamic Revolution in Iran, 1979; at which time the calendar was reverted to Solar Hijri.[3]

Afghanistan legally adopted the official Jalali calendar in 1922[1] but with different month names. The Dari Persian language in Afghanistan uses Dari names of the zodiacal signs, while the Pashto language in Afghanistan uses the Pashto names of the zodiacal signs. The Solar Hijri calendar is the official calendar of the government of Afghanistan, and all national holidays and administrative issues are fixed according to the Solar Hijri calendar.

The Solar Hijri calendar year begins at the start of Spring in the northern hemisphere: on the midnight between the two consecutive solar noons which include the instant of the Northern spring equinox, when the sun enters the northern hemisphere. Hence, the first noon is on the last day of one calendar year and the second noon is on the first day (Nowruz) of the next year.

The first day of the calendar year is also the day of the greatest festival of the year in Iran, Afghanistan and surrounding regions, called norooz (two morphemes: no (new) and rooz (day), meaning "new day"). The celebration is filled with many festivities and runs a course of 13 days. The last day of which is called siz-dah bedar (Literal translation-"13 to outdoor")

(*) The month names are the signs of Zodiac. They were used in Iran in early 20th century when the solar calendar was being used. The names are in fact the Arabic names for signs of Zodiac, please see دائرة البروج.

In the Iranian calendar, every week begins on Saturday and ends on Friday. The names of the days of the week are as follows: shambe (natively spelled "shanbeh", Persian: شنبه‎), yekshambe, doshambe, seshambe, chæharshambe, panjshambe and jom'e (yek, do, se, chæhar, and panj are the Persian words for the numbers one through five). The name for Friday, jom'e, is Arabic (Persian: جمعه‎). Jom'e is sometimes referred to by the native Persian name, adineh[ɒːdiːne] (Persian: آدینه‎). In most Islamic countries, Friday is the weekly holiday.

Calculating the day of the week is easy, using an anchor date. One good such date is Sunday, 1 Farvardin 1372, which equals 21 March 1993. Assuming the 33-year cycle approximation, move back by one weekday to jump ahead by one 33-year cycle. Similarly, to jump back by one 33-year cycle, move ahead by one weekday.

As in the Gregorian calendar, dates move forward exactly one day of the week with each passing year, except if there is an intervening leap day when they move two days. The anchor date 1 Farvardin 1372 is chosen so that its 4th, 8th, ..., 32nd anniversaries come immediately after leap days, yet the anchor date itself does not immediately follow a leap day.

The Solar Hijri year begins about 21 March of each Gregorian year and ends about 20 March of the next year. To convert the Solar Hijri year into the equivalent Gregorian year add 621 or 622 years to the Solar Hijri year depending on whether the Solar Hijri year has or has not begun.

Solar Hijri (Persian) calendar is one of the oldest calendars in the world, as well as the most accurate solar calendar in use today. Since the calendar uses astronomical calculation for determining the vernal equinox, it has no intrinsic error, but this makes it an observation based calendar.[6][7][8][9]Ahmad Birashk proposed an alternative means of determining leap years. His technique avoids the need to determine the moment of the astronomical equinox, replacing it with a very complex leap year structure. Years are grouped into cycles which begin with four normal years after which every fourth subsequent year in the cycle is a leap year. Cycles are grouped into grand cycles of either 128 years (composed of cycles of 29, 33, 33, and 33 years) or 132 years, containing cycles of 29, 33, 33, and 37 years. A great grand cycle is composed of 21 consecutive 128-year grand cycles and a final 132 grand cycle, for a total of 2820 years. The pattern of normal and leap years which began in 1925 will not repeat until the year 4745.

Each 2820 year great grand cycle contains 2137 normal years of 365 days and 683 leap years of 366 days, with the average year length over the great grand cycle of 365.24219852. This average is just 0.00000026 day shorter than the mean tropical year of 365.24219878 days, but differs considerably more from the mean vernal equinox year of 365.242362 days, which means that the new year, intended to fall on the vernal equinox, would drift by half a day over the course of a cycle.[2]